There is of course a range of opinions, and no doubt you may find some people who are upset enough about the prevalence of sexual assault and rape that they embrace strong rhetoric about, basically, assuming the accused party to be guilty until proven innocent. But it's still a very big step from such rhetoric to actually supporting the use of such standards in the criminal justice system, which would be blatantly illegal and unacceptable by the standards of the US or any other western nation.

However, I think I'm right in saying that for most people who embrace MeToo or BelieveAllWomen, the first priority is actually to change the way the accuser herself is treated in so many cases. Making sure that her complaint is taken seriously, that she is treated with respect and given a chance to talk about her experiences, knowing that memories from years ago are bound to be imperfect on some of the details. Hearing her out with an open mind and without trying to disprove the accusation the second some apparent discrepancy appears. In some cases, depending on who the accusations are against and how much media attention they get, protecting her from the waves of online abuse, trolling, doxxing, death threats that will inevitably follow.

None of those things would increase the risk of convicting someone who is wrongfully accused, since that requires actual proof. Sure, a person who is wrongfully accused would still suffer damage to their reputation, but then they could sue for libel or slander, if the accusation turns out in hindsight to have been intentionally false. Even so, I agree they might suffer permanent negative consequences in their social life, but then, so would the people falsely accused of any other crime who are found innocent - and, of course, the people who make accusations of sexual assault or rape that are widely disbelieved.

In the end it becomes a numbers game, what the greater risk is. If you somehow believe that the majority of sexual assault or rape accusations are plain false or wildly exaggerated, then it's normal enough that you are more concerned with the rights of the falsely accused than with ensuring that accusers are listened to in good faith. But all the evidence points the other way - that only a small minority of actual guilty people are convicted in the end, while intentionally false accusations are rare (though inevitably given a lot of attention whenever they occur).

Edit: Wanted to add that obviously it would often be impossible to prove that an accusation was intentionally false and made with malicious intent - but there, too, the principle of innocent unless proven guilty should apply, right? And since you are concerned not only with legal guilt and its legal consequences, but also with the judgements in the court of public opinion, perhaps you should also make sure not to assume that accusations are intentionally and maliciously false unless that's proven to be the case, and to persuade others to do likewise?